For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)°, what is the measure of each angle?
A. 15.3
B. 6
C. 29
D. 53
Two vertical angles are formed when two lines intersect. Vertical angles are always congruent, which means they have the same measure.
If m∠2 = (5x+23)° and m∠4 = (3x+35)°, this means that
(5x+23)° = (3x+35)°.
To solve for x, we can subtract 3x from both sides and subtract 23 from both sides:
(5x+23)° - 3x = (3x+35)° - 3x
2x + 23° = 35°
Subtracting 23° from both sides gives:
2x = 12°
Finally, divide both sides by 2:
x = 6°
Now that we have found the value of x, we can substitute it into either one of the angle measures to find the measure of each angle. Let's use m∠2:
m∠2 = (5x+23)°
m∠2 = (5(6)+23)°
m∠2 = (30+23)°
m∠2 = 53°
So, the measure of each angle is 53°.
Therefore, the answer is D. 53.